Question

Greta, an elderly investor, has a degree of risk aversion of A 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of one-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 6% per year, with a SD of 21%. The hedge fund risk premium is estimated at 11% with a SD of 36%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta is not fully convinced by this claim. What should be Greta's capital allocation? (Do not round your intermediate calculations. Round your answers to 2 decimal places.) S&P % Hedge Risk-free asset

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

C D Risk Premium Std. Deviation of return Correlation S&P 500 6.00% 21.00% 0.00 Hedge Fund 11.00% 36.00% Optimal risky Portfolio Portfolio invested in S&P 500 Portfolio invested in Hedge Fund Risk Premium of Optimal portfolio Std. deviation of Optimal portfolio 0.6158 0.3842 7.92% 18.93% Risk Aversion (A) 15 17 Allocation of Complete Portfolio Optimal risky Porfolio Risk free assets 18 0.7364 0.2636 19 Thus, Greta's Capital Allocation S&P Hedge Risk-free asset 45.35% 28.29% 26.36%

Cell reference -

S&P 500 Hedge Fund 0.11 Risk Premium Std. Deviation of return Correlation 0.06 0.21 0.36 Optimal risky Portfolio Portfolio invested in S&P 500 Portfolio invested in Hedge Fund Risk Premium of Optimal portfolio Std. deviation of Optimal portfolio =((C3)*D4^2-(D3)*C5*C4*D4)/((C3)*D4^2+(D3)*C4^2-(C3)+(D3))*C5*C4*D4) =1-09 =C9*C3+C10*D3 =SQRT((C9*C4)^2+(C10*D4)^2+2*C9*C10*C4*D4*C5) Risk Aversion (A) Allocation of Complete Portfolio Optimal risky Porfolio Risk free assets =C11/(C14*C1242) =1-C17 Thus, Greta's Capital Allocation S&P Hedge Risk-free asset =C17*C9 =C17*010 =C18 25

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